My thought is that these ministers should give them a ceremony that will convert them from their wicked ways. 4 hours of sermons on the evils of homosexuality and how they will end up in hell suffering eternal damnation and everlasting agony in hell should cause them to reconsider forcing the minister to marry them.
That would probably work, if they gave the same sermon for all their weddings. Might actually be a good idea. They could require pre-marriage counseling as part of the package.
But that might drive away 90% of their customers.....